Resultant Centrifugal Acceleration

M

MAC-A-TAC

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Please help.

a[sub:3m523wve]c[/sub:3m523wve]=?(-r?[sup:3m523wve]2[/sup:3m523wve])[sup:3m523wve]2[/sup:3m523wve]
Wouldn't the answer be a positive r?? My answer key shows -r?.

Thank you.
 
What is the question? What are you supposed to do with the posted equation? (And for what do the variables stand?)

Thank you! :D

Eliz.
 
Re: Resultant Centrifugal Acelleration

Actually, the way you have it, it should be:

\(\displaystyle a=\sqrt{(-rw^{2})^{2}}=|r|w^{2}\)
 
Re: Resultant Centrifugal Acelleration

r = radius and ? = angular velocity but this does not matter.
What should the sign of r? be once the square root sign is removed?

Thank you.
 
Re: Resultant Centrifugal Acelleration

Did I have it interpreted correctly?. If so, it is an absolute value for r.
 
Re: Resultant Centrifugal Acelleration

MAC-A-TAC said:
Please help.

a[sub:5bacezk4]c[/sub:5bacezk4]=?(-r?[sup:5bacezk4]2[/sup:5bacezk4])[sup:5bacezk4]2[/sup:5bacezk4]
Wouldn't the answer be a positive r?? My answer key shows -r?.

Thank you.
Click to expand...

Here you are calculating the magnitude of the acceleration (which is a vector).

The direction of vector (which determines + or - sign) would come from your definition of positive direction and the free-body diagram.
 
MAC-A-TAC said:
r = radius and ? = angular velocity but this does not matter.
Click to expand...


Your comment is wrong, Mac. The definition of symbols matters very much.

Firstly, now that you've explained the symbols, we can tell that r and w are separate symbols.

(Sometimes, the characters "rw" represent a single symbol, not a product.)

Secondly, since |r| denotes that the quantity represented by r can be either positive or negative, it's very important to know that the symbol r represents a LENGTH, and, therefore, can never be negative.

When discussing mathematics, it does matter very much that you be as clear as possible.

 
Re: Resultant Centrifugal Acelleration

Thank you all for the help.

?(-r?[sup:3grk7dl7]2[/sup:3grk7dl7])[sup:3grk7dl7]2[/sup:3grk7dl7] is the same as {(-r?[sup:3grk7dl7]2[/sup:3grk7dl7])[sup:3grk7dl7]2[/sup:3grk7dl7]}[sup:3grk7dl7]½[/sup:3grk7dl7].
½ x 2 = 1 thus the answer is negative r?[sup:3grk7dl7]2[/sup:3grk7dl7]. Sorry for the lack of clarity in my question but now you should be able to see what I was after.

Thanks again.
 
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